Endocardial mapping system

ABSTRACT

A system for mapping electrical activity of a patient&#39;s heart includes a set of electrodes spaced from the heart wall and a set of electrodes in contact with the heart wall. Voltage measurements from the electrodes are used to generate three-dimensional and two-dimensional maps of the electrical activity of the heart.

TECHNICAL FIELD

The invention discloses the apparatus and technique for forming athree-dimensional electrical map of the interior of a heart chamber, anda related technique for forming a two-dimensional subsurface map at aparticular location in the endocardial wall.

BACKGROUND ART

It is common to measure the electrical potentials present on theinterior surface of the heart as a part of an electrophysiologic studyof a patient's heart. Typically such measurements are used to form atwo-dimensional map of the electrical activity of the heart muscle. Anelectrophysiologist will use the map to locate centers of ectopicelectrical activity occurring within the cardiac tissues. Onetraditional mapping technique involves a sequence of electricalmeasurements taken from mobile electrodes inserted into the heartchamber and placed in contact with the surface of the heart. Analternative mapping technique takes essentially simultaneousmeasurements from a floating electrode array to generate atwo-dimensional map of electrical potentials.

The two-dimensional maps of the electrical potentials at the endocardialsurface generated by these traditional processes suffer many defects.Traditional systems have been limited in resolution by the number ofelectrodes used. The number of electrodes dictated the number of pointsfor which the electrical activity of the endocardial surface could bemapped. Therefore, progress in endocardial mapping has involved eitherthe introduction of progressively more electrodes on the mappingcatheter or improved flexibility for moving a small mapping probe withelectrodes from place to place on the endocardial surface. Directcontact with electrically active tissue is required by most systems inthe prior art in order to obtain well conditioned electrical signals. Anexception is a non-contact approach with spot electrodes. These spotelectrodes spatially average the electrical signal through their conicalview of the blood media. This approach therefore also produces onesignal for each electrode. The small number of signals from theendocardial wall will result in the inability to accurately resolve thelocation of ectopic tissue masses. In the prior art, iso-potentials areinterpolated and plotted on a rectilinear map which can only crudelyrepresent the unfolded interior surface of the heart. Suchtwo-dimensional maps are generated by interpolation processes which“fill in” contours based upon a limited set of measurements. Suchinterpolated two-dimensional maps have significant deficiencies. First,if a localized ectopic focus is between two electrode views such a mapwill at best show the ectopic focus overlaying both electrodes and allpoints in between and at worst will not see it at all. Second, the twodimensional map, since it contains no chamber geometry information,cannot indicate precisely where in the three dimensional volume of theheat chamber an electrical signal is located. The inability toaccurately characterize the size and location of ectopic tissuefrustrates the delivery of certain therapies such as “ablation”.

SUMMARY DISCLOSURE

In general the present invention provides a method for producing ahigh-resolution, three-dimensional map of electrical activity of theinside surface of a heart chamber.

The invention uses a specialized catheter system to obtain theinformation necessary to generate such a map.

In general the invention provides a system and method which permits thelocation of catheter electrodes to be visualized in thethree-dimensional map.

The invention may also be used to provide a two-dimensional map ofelectrical potential at or below the myocardial tissue surface.

Additional features of the invention will appear from the followingdescription in which the illustrative embodiment is set forth in detailin conjunction with the accompanying drawings. It should be understoodthat many modifications to the invention, and in particular to thepreferred embodiment illustrated in these drawings, may be made withoutdeparting from the scope of the invention.

FIG. 1 is a schematic view of the system.

FIG. 2 is a view of the catheter assembly placed in an endocardialcavity.

FIG. 3 is a schematic view of the catheter assembly.

FIG. 4 is a view of the mapping catheter with the deformable lead bodyin the collapsed position.

FIG. 5 is a view of the mapping catheter with the deformable lead bodyin the expanded position.

FIG. 6 is a view of the reference catheter.

FIG. 7 is a schematic view representing the display of thethree-dimensional map.

FIG. 8 is a side view of an alternate reference catheter.

FIG. 9 is a side view of an alternate reference catheter.

FIG. 10 is a perspective view of an alternate distal tip.

FIG. 11 is a schematic view representing the display of the subsurfacetwo-dimensional map.

FIG. 12 is a schematic flow chart of the steps in the method.

DETAILED DISCLOSURE

In general, the system of the present invention is used for mapping theelectrical activity of the interior surface of a heart chamber 80. Themapping catheter assembly 14 includes a flexible lead body 72 connectedto a deformable distal lead body 74. The deformable distal lead body 74can be formed into a stable space filling geometric shape afterintroduction into the heart cavity 80. This deformable distal lead body74 includes an electrode array 19 defining a number of electrode sites.The mapping catheter assembly 14 also includes a reference electrodepreferably placed on a reference catheter 16 which passes through acentral lumen 82 formed in the flexible lead body 72 and the distal leadbody 74. The reference catheter assembly 16 has a distal tip electrodeassembly 24 which may be used to probe the heart wall. This distalcontact electrode assembly 24 provides a surface electrical referencefor calibration. The physical length of the reference catheter 16 takenwith the position of the electrode array 19 together provide a referencewhich may be used to calibrate the electrode array 19. The referencecatheter 16 also stabilizes the position of the electrode array 19 whichis desirable.

These structural elements provide a mapping catheter assembly which canbe readily positioned within the heart and used to acquire highlyaccurate information concerning the electrical activity of the heartfrom a first set of preferably non-contact electrode sites and a secondset of in-contact electrode sites.

The mapping catheter assembly 14 is coupled to interface apparatus 22which contains a signal generator 32, and voltage acquisition apparatus30. Preferably, in use, the signal generator 32 is used to measure thevolumetric shape of the heart chamber through impedance plethysmography.This signal generator is also used to determine the position of thereference electrode within the heart chamber. Other techniques forcharacterizing the shape of the heart chamber may be substituted. Next,the signals from all the electrode sites on the electrode array 19 arepresented to the voltage acquisition apparatus 30 to derive athree-dimensional, instantaneous high resolution map of the electricalactivity of the entire heart chamber volume. This map is calibrated bythe use of a surface electrode 24. The calibration is both electricaland dimensional. Lastly this three-dimensional map, along with thesignal from an intramural electrode 26 preferably at the tip of thereference catheter 16, is used to compute a two-dimensional map of theintramural electrical activity within the heart wall. Thetwo-dimensional map is a slice of the heart wall and represents thesubsurface electrical activity in the heart wall itself.

Both of these “maps” can be followed over time which is desirable. Thetrue three-dimensional map also avoids the problem of spatial averagingand generates an instantaneous, high resolution map of the electricalactivity of the entire volume of the heart chamber and the endocardialsurface. This three-dimensional map is an order of magnitude moreaccurate and precise than previously obtained interpolation maps. Thetwo-dimensional map of the intramural slice is unavailable using priortechniques.

Hardware Description

FIG. 1 shows the mapping system 10 coupled to a patient's heart 12. Themapping catheter assembly 14 is inserted into a heart chamber and thereference electrode 24 touches the endocardial surface 18.

The preferred array catheter 20 carries at least twenty-four individualelectrode sites which are coupled to the interface apparatus 22. Thepreferred reference catheter 16 is a coaxial extension of the arraycatheter 20. This reference catheter 16 includes a surface electrodesite 24 and a subsurface electrode site 26 both of which are coupled tothe interface apparatus 22. It should be understood that the electrodesite 24 can be located directly on the array catheter. The arraycatheter 20 may be expanded into a known geometric shape, preferablyspherical. Resolution is enhanced by the use of larger sized sphericalshapes. A balloon 77 or the like should be incorporated under theelectrode array 19 to exclude blood from the interior of the electrodearray 19. The spherical shape and exclusion of blood are not requiredfor operability but they materially reduce the complexity of thecalculations required to generate the map displays.

The reference electrode 24 and/or the reference catheter 16 servesseveral purposes. First they stabilize and maintain the array 19 at aknown distance from a reference point on the endocardial surface 18 forcalibration of the shape and volume calculations. Secondly, the surfaceelectrode 24 is used to calibrate the electrical activity measurementsof the endocardial surface 18 provided by the electrode array 19.

The interface apparatus 22 includes a switching assembly 28 which is amultiplexor to sequentially couple the various electrode sites to thevoltage acquisition apparatus 30, and the signal generator apparatus 32.These devices are under the control of a computer 34. The voltageacquisition apparatus 30 is preferably a 12 bit A to D convertor. Asignal generator 32 is also supplied to generate low current pulses fordetermining the volume and shape of the endocardial chamber usingimpedance plethysmography, and for determining the location of thereference catheter.

The computer 34 is preferably of the “workstation” class to providesufficient processing power to operate in essentially real time. Thiscomputer operates under the control of software set forth in the flowchart of FIG. 12.

Catheter Description

FIG. 2 shows a portion of the mapping catheter assembly 14 placed into aheart chamber 80. The mapping catheter assembly 14 includes a referencecatheter 16 and an array catheter 20. In FIG. 2 the array catheter 20has been expanded through the use of a stylet 92 to place the electrodearray 19 into a stable and reproducible geometric shape. The referencecatheter 16 has been passed through the lumen 82 of the array catheter20 to place a distal tip electrode assembly 24 into position against anendocardial surface. In use, the reference catheter 16 provides amechanical location reference for the position of the electrode array19, and the tip electrode assembly 24 provides an electrical potentialreference at or in the heart wall for the mapping process.

Although the structures of FIG. 1 are preferred there are severalalternatives within the scope of the invention. The principle objectiveof the preferred form of the catheter system is to reliably place aknown collection of electrode sites away from the endocardial surface,and one or more electrode sites into contact with the endocardium. Thearray catheter is an illustrative structure for placing at least some ofthe electrode sites away from the endocardial surface. The arraycatheter itself can be designed to mechanically position one or moreelectrode sites on the endocardial surface. The reference catheter is apreferred structure for carrying one or more electrode sites and may beused to place these electrode sites into direct contact with theendocardial surface.

It should be understood that the reference catheter could be replacedwith a fixed extension of the array catheter and used to push a segmentof the array onto the endocardial surface. In this alternate embodimentthe geometric shape of the spherical array maintains the otherelectrodes out of contact with the endocardial surface.

FIG. 3 shows the preferred construction of the mapping catheter assembly14 in exaggerated scale to clarify details of construction. In general,the array catheter 20 includes a flexible lead body 72 coupled to adeformable lead body 74. The deformable lead body 74 is preferably abraid 75 of insulated wires, several of which are shown as wire 93, wire94, wire 95 and wire 96. An individual wire such as 93 may be traced inthe figure from the electrical connection 79 at the proximal end 81 ofthe flexible lead body 72 through the flexible lead body 72 to thedistal braid ring 83 located on the deformable lead body 74. At apredetermined location in the deformable lead body 74 the insulation hasbeen selectively removed from this wire 93 to form a representativeelectrode site 84. Each of the several wires in the braid 75 maypotentially be used to form an electrode site. Preferably all of thetypically twenty-four to one-hundred-twenty-eight wires in the braid 75are used to form electrode sites. Wires not used as electrode sitesprovide mechanical support for the electrode array 19. In general, theelectrode sites will be located equidistant from a center defined at thecenter of the spherical array. Other geometrical shapes are usableincluding ellipsoidal and the like.

The proximal end 81 of the mapping catheter assembly 14 has suitableelectrical connection 79 for the individual wires connected to thevarious electrode sites. Similarly the proximal connector 79 can have asuitable electrical connection for the distal tip electrode assembly 24of the reference catheter 16 or the reference catheter 16 can use aseparate connector. The distance 90 between the electrode array 19 andthe distal tip assembly 24 electrode can preferentially be varied bysliding the reference catheter through the lumen 82, as shown by motionarrow 85. This distance 90 may be “read” at the proximal end 81 bynoting the relative position of the end of the lead body 72 and theproximal end of the reference catheter 16.

FIG. 4 is a view of the mapping catheter with the deformable lead body74 in the collapsed position.

FIG. 5 shows that the wire stylet 92 is attached to the distal braidring 83 and positioned in the lumen 82. Traction applied to the distalbraid ring 83 by relative motion of the stylet 92 with respect to thelead body 72 causes the braid 75 to change shape. In general, tractioncauses the braid 75 to move from a generally cylindrical form seen inFIG. 4 to a generally spherical form seen best in FIG. 2 and FIG. 5.

The preferred technique is to provide a stylet 92 which can be used topull the braid 75 which will deploy the electrode array 19. However,other techniques may be used as well including an optional balloon 77shown as in FIG. 3, which could be inflated under the electrode array 19thereby causing the spherical deployment of the array 19. Modificationof the braid 75 can be used to control the final shape of the array 19.For example an asymmetrical braid pattern using differing diameter wireswithin the braid can preferentially alter the shape of the array. Themost important property of the geometric shape is that it spaces theelectrode sites relatively far apart and that the shape be predictablewith a high degree of accuracy.

FIG. 6 shows a first embodiment of the reference catheter 16 where thedistal electrode assembly 24 is blunt and may be used to make a surfacemeasurement against the endocardial surface. In this version of thecatheter assembly the wire 97 (FIG. 2) communicates to the distal tipelectrode and this wire may be terminated in the connector 79.

FIG. 8 shows an alternate reference catheter 98 which is preferred ifboth surface and/or subsurface measurements of the potential proximatethe endocardial surface are desired. This catheter 98 includes both areference electrode 24 and an extendable intramural electrode body 100.

FIG. 9 illustrates the preferred use of an intramural electrode stylet101 to retract the sharp intramural electrode body 100 into thereference catheter lead body 102. Motion of the intramural electrodebody 100 into the lead body 102 is shown by arrow 103.

FIG. 10 shows the location of the intramural electrode site 26 on theelectrode body 100. It is desirable to use a relatively small electrodesite to permit localization of the intramural electrical activity.

The array catheter 20 may be made by any of a variety of techniques. Inone method of manufacture, the braid 75 of insulated wires 93,94,95,96can be encapsulated into a plastic material to form the flexible leadbody 72. This plastic material can be any of various biocompatiblecompounds with polyurethane being preferred. The encapsulation materialfor the flexible lead body 72 is selected in part for its ability to beselectively removed to expose the insulated braid 75 to form thedeformable lead body 74. The use of a braid 75 rather than a spiralwrap, axial wrap, or other configuration inherently strengthens andsupports the electrodes due to the interlocking nature of the braid.This interlocking braid 75 also insures that, as the electrode array 19deploys, it does so with predictable dimensional control. This braid 75structure also supports the array catheter 20 and provides for thestructural integrity of the array catheter 20 where the encapsulatingmaterial has been removed.

To form the deformable lead body 74 at the distal end of the arraycatheter 20, the encapsulating material can be removed by knowntechniques. In a preferred embodiment this removal is accomplished bymechanical removal of the encapsulating material by grinding or thelike. It is also possible to remove the material with a solvent. If theencapsulating material is polyurethane, tetrahydrofuran or cyclohexanonecan be used as a solvent. In some embodiments the encapsulating materialis not removed from the extreme distal tip to provide enhancedmechanical integrity forming a distal braid ring 83.

With the insulated braid 75 exposed, to form the deformable lead body 74the electrodes sites can be formed by removing the insulation over theconductor in selected areas. Known techniques would involve mechanical,thermal or chemical removal of the insulation followed by identificationof the appropriate conducting wire at the proximal connector 79. Thismethod makes it difficult to have the orientation of the proximalconductors in a predictable repeatable manner. Color coding of theinsulation to enable selection of the conductor/electrode is possiblebut is also difficult when large numbers of electrodes are required.Therefore it is preferred to select and form the electrode array throughthe use of high voltage electricity. By applying high voltageelectricity (typically 1-3 KV) to the proximal end of the conductor anddetecting this energy through the insulation it is possible tofacilitate the creation of the electrode on a known conductor at adesired location. After localization, the electrode site can be createdby removing insulation using standard means or by applying a highervoltage (eg. 5 KV) to break through the insulation.

Modifications can be made to this mapping catheter assembly withoutdeparting from the teachings of the present invention. Accordingly thescope of the invention is only to be limited only by the accompanyingclaims.

Software Description

The illustrative method may be partitioned into nine steps as shown inFIG. 12. The partitioning of the step-wise sequence is done as an aid toexplaining the invention and other equivalent partitioning can bereadily substituted without departing from the scope of the invention.

At step 41 the process begins. The illustrative process assumes that theelectrode array assumes a known spherical shape within the heartchamber, and that there are at least twenty-four electrodes on theelectrode array 19. This preferred method can be readily modified toaccommodate unknown and non-reproducible, non-spherical shaped arrays.The location of each of these electrode sites on the array surface isknown from the mechanical configuration of the displayed array. A methodof determining the location of the electrode array 19 and the locationof the heart chamber walls (cardiac geometry) must be available. Thisgeometry measurement (options include ultrasound or impedanceplethysmography) is performed in step 41. If the reference catheter 16is extended to the chamber wall 18 then its length can be used tocalibrate the geometry measurements since the calculated distance can becompared to the reference catheter length. The geometry calculations areforced to converge on the known spacing represented by the physicaldimensions of the catheters. In an alternative embodiment referenceelectrode 24 is positioned on array catheter 20 and therefore itsposition would be known.

In step 42 the signals from all the electrode sites in the electrodearray 19 are sampled by the A to D converter in the voltage acquisitionapparatus 30. These measurements are stored in a digital file for lateruse in following steps. At this point (step 43) the known locations ofall the electrodes on the electrode array 19 and the measured potentialsat each electrode are used to create the intermediate parameters of thethree-dimensional electrical activity map. This step uses field theorycalculations presented in greater detail below. The components which arecreated in this step (Φ_(lm)) are stored in a digital file for later usein following steps.

At the next stage the question is asked whether the reference catheter16 is in a calibrating position. In the calibrating position, thereference catheter 16 projects directly out of the array catheter 20establishing a length from the electrode array 19 which is a knowndistance from the wall 18 of the heart chamber. This calibrationposition may be confirmed using fluoroscopy. If the catheter is not inposition then the process moves to step 45, 46 or 47.

If the reference catheter 16 is in the calibrating position then in step44 the exact position of the reference catheter 16 is determined usingthe distance and orientation data from step 41. The availableinformation includes position in space of the reference catheter 16 onthe chamber wall 18 and the intermediate electrical activity mapparameters of the three-dimensional map. Using these two sets ofinformation the expected electrical activity at the reference cathetersurface electrode site 24 is determined. The actual potential at thissite 24 is measured from the reference catheter by the A to D converterin the voltage acquisition apparatus 30. Finally, a scale factor isadjusted which modifies the map calculations to achieve calibratedresults. This adjustment factor is used in all subsequent calculationsof electrical activity.

At step 47 the system polls the user to display a three-dimensional map.If such a map is desired then a method of displaying the electricalactivity is first determined. Second an area, or volume is defined forwhich the electrical activity is to be viewed. Third a level ofresolution is defined for this view of the electrical activity. Finallythe electrical activity at all of the points defined by the displayoption, volume and resolution are computed using the field theorycalculations and the adjustment factor mentioned above. These calculatedvalues are then used to display the data on computer 34.

FIG. 7 is a representative display 71 of the output of process 47. Inthe preferred presentation the heart is displayed as a wire grid 36. Theiso-potential map for example is overlaid on the wire grid 36 andseveral iso-potential lines such as iso-potential or isochrone line 38are shown on the drawing. Typically the color of the wire grid 36 andthe iso-potential or isochrone lines will be different to aidinterpretation. The potentials may preferably be presented by acontinuously filled color-scale rather than iso-potential or isochronelines. The tightly closed iso-potential or isochrone line 39 may arisefrom an ectopic focus present at this location in the heart. In therepresentative display 71 of process 47 the mapping catheter assemblywill not be shown.

In step 45 a subthreshold pulse is supplied to the surface electrode 24of the reference catheter 16 by the signal generator 32. In step 54 thevoltages are measured at all of the electrode sites on the electrodearray 19 by the voltage acquisition apparatus 30 One problem in locatingthe position of the subthreshold pulse is that other electrical activitymay render it difficult to detect. To counteract this problem step 55starts by subtracting the electrical activity which was just measured instep 44 from the measurements in step 54. The location of the tip of thereference catheter 16 (i.e. surface electrode 24), is found by firsterforming the same field theory calculations of step 45 on this derivedelectrode data. Next, four positions in pace are defined which arepositioned near the heart chamber walls. The potentials at these sitesare calculated using the three-dimensional electrical activity map.These potentials are then used to triangulate, and thus determine, theposition of the subthreshold pulse at the surface electrode 24 of thereference catheter 16. If more accurate localization is desired thenfour more points which are much closer to the surface electrode 24 canbe defined and the triangulation can be performed again. This procedurefor locating the tip of the reference catheter 16 can be performedwhether the surface electrode 24 is touching the surface or is locatedin the blood volume and is not in contact with the endocardial surface.

At step 48 the reference catheter's position in space can be displayedby superimposing it on the map of electrical activity created in step47. An example of such a display 71 is presented in FIG. 7.

When step 46 is reached the surface electrode 24 is in a known positionon the endocardial surface 18 of the heart chamber which is proper fordetermining the electrical activity of the tissue at that site. If theintramural or subsurface extension 100 which preferentially extends fromthe tip of the reference catheter 102 is not inserted into the tissuethen the user of the system extends the subsurface electrode 26 into thewall 18. The potentials from the surface electrode 24 and from theintramural subsurface 26 electrode are measured by voltage acquisitionapparatus 30. Next a line 21 along the heart chamber wall which has thesurface electrode 24 at its center is defined by the user of the system.The three-dimensional map parameters from step 43 are then used tocompute a umber of points along this line including the site of hereference catheter surface electrode 24. These alculations are adjustedto conform to the measured alue at the reference catheter surfaceelectrode 24. ext a slice of tissue is defined and bounded by this line21 (FIG. 7) and the location of the intramural subsurface electrode 26(FIG. 11) and computed positions such as 23 and 25. Subsequently atwo-dimensional map 27 of the electrical activity of this slice oftissue is computed using the center of gravity calculations detailedbelow in the section on algorithm descriptions. Points outside of theboundary of the slice cannot be computed accurately. In step 49 this map27 of electrical activity within the two-dimensional slice is displayedas illustrated in FIG. 11. In this instance the iso-potential line 17indicates the location within the wall 18 of the ectopic focus.

Description of the Preferred Computing Algorithms

Two different algorithms are suitable for implementing different stagesof the present invention.

The algorithm used to derive the map of the electrical activity of theheart chamber employs electrostatic volume-conductor field theory toderive a high resolution map of the chamber volume. The second algorithmis able to estimate intramural electrical activity by interpolatingbetween points on the endocardial surface and an intramural measurementusing center of gravity calculations.

In use, the preliminary process steps identify the position of theelectrode array 19 consequently the field theory algorithm can beinitialized with both contact and non-contact type data. This is onedifference from the traditional prior art techniques which requireeither contact or non-contact for accurate results, but cannotaccommodate both. This also permits the system to discern the differencebetween small regions of electrical activity close to the electrodearray 19 from large regions of electrical activity further away from theelectrode array 19.

In the first algorithm, from electrostatic volume-conductor field theoryit follows that all the electrodes within the solid angle view of everylocus of electrical activity on the endocardial surface are integratedtogether to reconstruct the electrical activity at any given locusthroughout the entire volume and upon the endocardium. Thus as bestshown in FIG. 7 the signals from the electrode array 19 on the catheter20 produce a continuous map of the whole endocardium. This is anotherdifference between the present method and the traditional prior artapproach which use the electrode with the lowest potential as theindicator of cardiac abnormality. By using the complete information inthe algorithm, the resolution of the map shown in FIG. 7 is improved byat least a factor of ten over prior methods. Other improvements include:the ability to find the optimal global minimum instead of sub-optimallocal minima; the elimination of blind spots between electrodes; theability to detect abnormalities caused by multiple ectopic foci; theability to distinguish between a localized focus of electrical activityat the endocardial surface and a distributed path of electrical activityin the more distant myocardium; and the ability to detect other types ofelectrical abnormalities including detection of ischemic or infarctedtissue.

The algorithm for creating the 3D map of the cardiac volume takesadvantage of the fact that myocardial electrical activityinstantaneously creates potential fields by electrotonic conduction.Since action potentials propagate several orders of magnitude slowerthan the speed of electrotonic conduction, the potential field isquasi-static. Since there are no significant charge sources in the bloodvolume, Laplace's Equation for potential completely describes thepotential field in the blood volume:

{overscore (v)}Φ=0

LaPlace's equation can be solved numerically or analytically. Suchnumerical techniques include boundary element analysis and otherinterative approaches comprised of estimating sums of nonlinearcoefficients.

Specific analytical approaches can be developed based on the shape ofthe probe (i.e. spherical, prolate spherical or cylindrical). Fromelectrostatic field theory, the general spherical harmonic seriessolution for potential is:${\varphi \left( {r,\theta,\phi} \right)} = {\sum\limits_{\infty}^{l = 0}{\sum\limits_{m = {- l}}^{l}{\left\{ {{A_{1}r^{1}} + {B_{1}r^{- {({l - 1})}}}} \right\} \varphi_{lm}{Y_{lm}\left( {\theta,\phi} \right)}}}}$

In spherical harmonics, Y_(lm)(θ, ψ) is the spherical harmonic seriesmade up of Legendre Polynomials. Φ_(lm) is the lm^(th) component ofpotential and is defined as:

φ_(lm)=∫V(θ, ψ)Y _(lm)(θ, ψ)dΩ

where V(θ, φ) is the measured potential over the probe radius R and dΩis the differential solid angle and, in spherical coordinates, isdefined as:

dΩ=sin θdθdψ

During the first step in the algorithmic determination of the 3D map ofthe electrical activity each Φlm component is determined by integratingthe potential at a given point with the spherical harmonic at that pointwith respect to the solid angle element subtended from the origin tothat point. This is an important aspect of the 3D map; its accuracy increating the 3D map is increased with increased numbers of electrodes inthe array and with increased size of the spherical array. In practice itis necessary to compute the Φ_(lm) components with the subscript set to4 or greater. These Φ_(lm) components are stored in an 1 by m array forlater determination of potentials anywhere in the volume within theendocardial walls.

The bracketed expression of equation 1 (in terms of A₁, B₁, and r)simply contains the extrapolation coefficients that weight the measuredprobe components to obtain the potential components anywhere in thecavity. Once again, the weighted components are summed to obtain theactual potentials. Given that the potential is known on the probeboundary, and given that the probe boundary is non-conductive, we candetermine the coefficients A₁ and B₁, yielding the following finalsolution for potential at any point within the boundaries of the cavity,using a spherical probe of radius R:${\varphi \left( {r,\theta,\phi} \right)} = {\sum\limits_{l = 0}^{\infty}{\sum\limits_{m = {- 1}}^{l}{\left\lbrack {{\left( \frac{l + 1}{{2l} + 1} \right)\quad \left( \frac{r}{R} \right)^{1}} + {\left( \frac{l}{{2l} + 1} \right)\left( \frac{r}{R} \right)^{{- l} - 1}}} \right\rbrack \varphi_{lm}{Y_{lm}\left( {\theta,\phi} \right)}}}}$

on exemplary method for evaluating the integral for Φ_(lm) is thetechnique of Filon integration with an estimating sum, discretized by platitudinal rows and q longitudinal columns of electrodes on thespherical probe.$\varphi_{lm} \geq {\frac{4\pi}{pq}{\sum\limits_{i = 1}^{p}{\sum\limits_{j = 1}^{q}{{V\left( {\theta_{i},\phi_{j}} \right)}{Y_{lm}\left( {\theta_{i},\phi_{j}} \right)}}}}}$

Note that p times q equals the total number of electrodes on thespherical probe array. The angle θ ranges from zero to π radians and ψranges from zero to 2π radians.

At this point the determination of the geometry of the endocardial wallsenters into the algorithm. The potential of each point on theendocardial wall can now be computed by defining them as r, θ, and ψ.During the activation sequence the graphical representation of theelectrical activity on the endocardial surface can be slowed down by 30to 40 times to present a picture of the ventricular cavity within a timeframe useful for human viewing.

A geometric description of the heart structure is required in order forthe algorithm to account for the inherent effect of spatial averagingwithin the medium (blood). Spatial averaging is a function of both theconductive nature of the medium as well as the physical dimensions ofthe medium.

Given the above computed three-dimensional endocardial potential map,the intramural activation map of FIG. 11 is estimated by interpolatingbetween the accurately computed endocardial potentials at locations 23and 25 (FIG. 7), and actual recorded endocardial value at the surfaceelectrode 24 and an actual recorded intramural value at the subsurfaceelectrode 26 site. This first-order estimation of the myocardialactivation map assumes that the medium is homogenous and that the mediumcontains no charge sources. This myocardial activation estimation islimited by the fact that the myocardial medium is not homogeneous andthat there are charge sources contained within the myocardial medium. Ifmore than one intramural point was sampled the underlying map ofintramural electrical activity could be improved by interpolatingbetween the endocardial surface values and all the sample intramuralvalues. The center-of-gravity calculations can be summarized by theequation:${V\left( \overset{\_}{r_{x}} \right)} = \frac{\sum\limits_{i = 1}^{n}{V_{i}\left( {{\overset{\_}{r_{x}} - \overset{\_}{r_{i}}}}^{- k} \right)}}{\sum\limits_{i = 1}^{n}{{\overset{\_}{r_{x}} - \overset{\_}{r_{i}}}}^{- k}}$

where, V(_(x)) represents the potential at any desired point defined bythe three-dimensional vector _(x) and, V_(i) represents each of n knownpotentials at a point defined by the three-dimensional vector _(i) and,k is an exponent that matches the physical behavior of the tissuemedium.

From the foregoing description, it will be apparent that the method fordetermining a continuous map of the electrical activity of theendocardial surface of the present invention has a number of advantages,some of which have been described above and others of which are inherentin the invention. Also modifications can be made to the mapping probewithout departing from the teachings of the present invention.Accordingly the scope of the invention is only to be limited asnecessitated by the accompanying claims.

We claim:
 1. An endocardial mapping catheter assembly comprising: (a) aplurality of insulated wires braided throughout their length into aninterlocking weave; (b) a distal portion of the interlocking weave beingexpandable from a first generally cylindrical shape to a second expandedshape; and (c) a plurality of electrodes on the distal portion of theinsulated wires, each electrode in electrical communication with asingle wire, and with each wire being in electrical communication withno more than a single electrode.
 2. The endocardial mapping catheterassembly of claim 1, further comprising d) an electrical plug on theproximal end of the interlocking weave, the electrical plug having aplurality of connections, each in electrical communication through oneof the insulated wires to one of the electrodes.
 3. The endocardialmapping catheter assembly of claim 1, wherein the interlocking weavefurther comprises a proximal non-expanding portion having a generallycylindrical shape.
 4. The endocardial mapping catheter assembly of claim3, wherein the proximal non-expanding portion is encapsulated in abiocompatible material.
 5. The endocardial mapping catheter assembly ofclaim 4 wherein the biocompatible material is polyurethane.
 6. Theendocardial mapping catheter assembly of claim 4 wherein the distalexpanding portion is not encapsulated in the biocompatible material. 7.The endocardial mapping catheter assembly of claim 1 wherein the secondexpanded shape is generally spherical.
 8. The endocardial mappingcatheter assembly of claim 1 wherein there are at least twenty-fourelectrodes.
 9. The endocardial mapping catheter assembly of claim 1further comprising an expandable balloon within the expandable distalportion of the wires.
 10. An endocardial mapping catheter assemblycomprising (a) an elongated flexible lead body having an interior lumenand proximal and distal ends; (b) at least twenty-four insulated wiresin the lumen extending from the proximal to the distal end of the leadbody, the wires collectively being braided together to form a wireassembly; (c) an expandable portion of the wire assembly near the distalend of the flexible lead body, the expandable portion being expandablefrom a first generally cylindrical shape to a second expanded shape; (d)the majority of wires in the wire assembly each having a singleelectrode in the expandable portion of the wire assembly; (e) anelectrical plug on the proximal end of the flexible lead body, theelectrical plug having a plurality of connections, each connection beingin electrical communication with one of the wires.
 11. An endocardialmapping catheter assembly comprising: (a) a plurality of insulated wiressurrounded by an insulating material, (b) a braid comprised of acombination of the insulated wires in an interlocking weave, (c) aflexible material surrounding a first portion of the braid, forming aflexible lead body, the flexible material not surrounding a secondportion of the braid, the second portion of the braid forming an array,the array being deformable into a predictable geometric shape, (d) atleast twenty-four electrodes on the braided wire array, each electrodein electronic communication with a single wire in the array.
 12. Thecatheter assembly of claim 11 wherein the electrode is a gap in theinsulating material surrounding the wire.
 13. The catheter assembly ofclaim 11, wherein the flexible material is polyurethane.
 14. Thecatheter assembly of claim 11, further comprising e) an expandableballoon within the array.
 15. The catheter assembly of claim 11, whereinthe braid forms a lumen.
 16. The catheter assembly of claim 15 furthercomprising a reference catheter in the lumen, the reference catheterhaving a tip electrode.
 17. The catheter assembly of claim 16 whereinthe reference catheter is movable relative to the braid within thelumen.
 18. The catheter assembly of claim 17, further comprising e) anelectrical connector adapted for connection to an external monitoringdevice, the tip electrode of the reference catheter as well as each wirein the braid having an electrode being in electrical communication witha particular location on the electrical connector.
 19. The catheterassembly of claim 11, further comprising e) an electrical connectoradapted for connection to an external monitoring device, each wire inthe braid having an electrode being in electrical communication with aparticular location on the electrical connector.